Ethylene acrylic acid copolymer, and the hair colorant composition which includes the water dispersing element which includes the metallocene catalyst polyolefine optionally, the metallocene catalyst polyolefine and the water dispersing element which includes ethylene acrylic acid copolymer, being the method of decreasing the hair damage by the hair colorant, it states the method of including the fact that it can soak the metallocene catalyst polyolefine and the water dispersing element which includes ethylene acrylic acid copolymer in the hair colorant.エチレンアクリル酸コポリマー、および任意にメタロセン触媒ポリオレフィンを含む水性分散体を含むヘア着色剤組成物、メタロセン触媒ポリオレフィンおよびエチレンアクリル酸コポリマーを含む水性分散体、ヘア着色剤によるヘアダメージを低減する方法であってメタロセン触媒ポリオレフィンおよびエチレンアクリル酸コポリマーを含む水性分散体をヘア着色剤中に含ませることを含む方法を記載する。